Closing the Gap

The Quest to Understand Prime Numbers

Vicky Neale

Looks not only at the breakthroughs on the Twin Primes Conjecture, but also the public collaboration aspects of the Polymath8 project

Plenty of visual imagery and sketches to illustrate key ideas

Provides a glimpse into how the international mathematical community works

Closing the Gap

The Quest to Understand Prime Numbers

Vicky Neale

Description

In 2013, a little known mathematician in his late 50s stunned the mathematical community with a breakthrough on an age-old problem about prime numbers. Since then, there has been further dramatic progress on the problem, thanks to the efforts of a large-scale online collaborative effort of a type that would have been unthinkable in mathematics a couple of decades ago, and the insight and creativity of a young mathematician at the start of his career.

Prime numbers have intrigued, inspired and infuriated mathematicians for millennia. Every school student studies prime numbers and can appreciate their beauty, and yet mathematicians' difficulty with answering some seemingly simple questions about them reveals the depth and subtlety of prime numbers.

Vicky Neale charts the recent progress towards proving the famous Twin Primes Conjecture, and the very different ways in which the breakthroughs have been made: a solo mathematician working in isolation and obscurity, and a large collaboration that is more public than any previous collaborative effort in mathematics and that reveals much about how mathematicians go about their work. Interleaved with this story are highlights from a significantly older tale, going back two thousand years and more, of mathematicians' efforts to comprehend the beauty and unlock the mysteries of the prime numbers.

Closing the Gap

The Quest to Understand Prime Numbers

Vicky Neale

Table of Contents

1. Introduction2. What is a prime?3. May 20134. It's easy to ask hard questions5. May 20136. Making hard problems easier7. June 20138. How many primes are there?9. July 201310. What's so mathematical about my mathematical pencil?11. August 201312. If primes are hard, let's try something else13. November 201314. Generalise . . .15. April 201416. Where next?

Closing the Gap

The Quest to Understand Prime Numbers

Vicky Neale

Author Information

Vicky Neale, Whitehead Lecturer, Oxford University

Vicky Neale is the Whitehead Lecturer at the Mathematical Institute and Balliol College, University of Oxford. A substantial part of her remit is public communication of mathematics. She has wide experience of working with students of all ages (school children to adults, via undergraduates), and of giving public lectures, and does various media work.

Closing the Gap

The Quest to Understand Prime Numbers

Vicky Neale

Reviews and Awards

"Neale writes in an inviting style that draws readers into this challenging subject, convincing them that, with a little effort, they too can follow along. An enjoyable book and journey, complemented by a helpful reading list and index... Recommended." -- CHOICE

"Closing the Gapis an excellent exposition of the study of prime numbers. Not only do we learn about the history of this area since the Greeks, but the book is the first aimed at a lay readership that provides insight into recent breakthroughs. Vicky Neale's passion in the subject is contagious and I enjoyed how she weaves together the mathematics with background on how mathematicians now work, as well as her reflections on what it is like to be a mathematician. This book would be ideal for a curious sixth former wanting to peek ahead at what might lie around the corner if they are considering studying mathematics at a higher level." -- Alex Bellos, author of Alex's Adventures in Numberland and Alex Through the Looking-Glass

"Her prose is clear but not patronizing, precise but accessible. The result is a very enjoyable book that can be read with profit not only by laypeople but also by mathematics students and the people who teach them." -- MAA Reviews

"Closing The Gap has gone straight into my top ten books to give to interested students... The book's introduction starts with an extended analogy comparing mathematics to climbing [and] Neale sets herself up as this guide, and succeeds brilliantly." -- The Aperiodical

"Closing the Gap is among the clearest popular accounts of maths I've read in a while. It's about prime numbers, as the title suggests, but it's also a master piece in the art of weaving. Apart from exploring the mathematics, the book gives an intimate description of the process of doing maths as experienced by those who do it every day, and an account of a particularly exciting, and recent, period when prime number theory made some great leaps forward. And it's a look at a completely new way of doing mathematics: in large online collaborations that anyone can join." -- PLUS

Closing the Gap

The Quest to Understand Prime Numbers

Vicky Neale

From Our Blog

When a group of people collectively solve a jigsaw puzzle, who gets the credit? The person who puts the final piece in the puzzle? The person who sorted out the edge pieces at the beginning? The person who realised what the picture was of? The person who found the puzzle pieces and suggested trying to put them together? The person who managed the project and kept everyone on track? The whole group?